Question

an employee claims that 20% of the email she receives is personal, 60% is work related, and 20% is spam. the high level of spam she is receiving is frustrating, so she creates some new filters. she then selects a random sample of 50 emails over the next several weeks. she would like to know if the distribution of emails she receives has changed. what are the appropriate hypotheses?
o ( h_{0} ): the distribution of emails received is no longer 20% personal, 60% work related, and 20% spam.
( h_{a} ): the distribution of emails received is still 20% personal, 60% work related, and 20% spam.
o ( h_{0} ): the distribution of emails received is still 20% personal, 60% work related, and 20% spam.
( h_{a} ): the distribution of emails received is no longer 20% personal, 60% work related, and 20% spam.
o ( h_{0} ): the distribution of emails received is still 20% personal, 60% work related, and 20% spam.
( h_{a} ): she now receives less than 20% spam.
o ( h_{0} ): the distribution of emails received is still 20% personal, 60% work related, and 20% spam.
( h_{a} ): she now receives an amount different from 20% spam.

Explanation:

In hypothesis testing, the null hypothesis \(H_0\) represents the status - quo or the assumed distribution. Here, the assumed distribution (before checking if it has changed) is 20% personal, 60% work - related, and 20% spam. The alternative hypothesis \(H_a\) is what we are trying to find evidence for. Since we want to know if the distribution has changed (not just about the spam percentage in a one - sided way like "less than" or a single - category change), it is a general change in the distribution.

Answer:

\(H_0\): The distribution of emails received is still 20% personal, 60% work related, and 20% spam. \(H_a\): The distribution of emails received is no longer 20% personal, 60% work related, and 20% spam.